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Direct Computation of the Oda Fractured Rock Mass Permeability Tensor From Digital Outcrop Datasets


Computation of the permeability tensor of a fractured rock mass is of considerable application within exploration and production. Fractures provide the locus of fluid flow and production within carbonate and unconventional reservoirs, but also present major challenges within the E&P value chain, often resulting in thief zones and sub-optimum production. Consequently, predicting and numerically representing the fluid flow properties of fractured reservoirs is a major component of many reservoir characterization and modeling workflows. With respect to the model representation of fracture systems, it is common practice to generate an initial discrete object based statistical representation of the discontinuity array (discrete fracture network: DFN). Due to the large computational expense of direct flow simulation on DFNs, this object model is usually then upscaled to a grid based porosity-permeability model, under the assumption of continuum like fracture network petrophysical properties. Two commonly applied upscaling methods exist; namely the Oda tensor method, which is geometrically based (dependent upon fracture size, orientation and aperture), and flow based methods, whereby grid block edge fracture transmissibilities are resolved using single phase flow simulations on the underlying DFN. Generally, the Oda Tensor method is computationally inexpensive, but does not account for fracture interconnectivity, whereas flow based methods consider such relationships explicitly at the cost of higher computation times. Though the merits and disadvantages of upscaling methods have subject to extensive debate, the medium upon which equivalent porous medium properties are computed has remained constant (i.e. stochastic DFNs conditioned by outcrop size and orientation statistics). In the present work, near-deterministic DFNs constrained to exposed fracture trace patterns are used as the basis for fracture permeability calculations. The method uses a moving window spatial search across a digital outcrop model surface to derive per-vertex calculations of the Oda permeability tensor, based upon the fracture normals, apertures and areas captured within the search domain. This analysis produces a spatially resolved vertex property field of fracture permeability which can be used as the basis for geostatistical modelling of fractured rock mass petrophysical properties, foregoing the need to build an intermediary idealized DFN using fracture survey data. The approach is demonstrated using naturally fractured exposures of the Dammam Formation, Qatar.